Analysis of a dynamic contact problem with long memory

We examine a mathematical framework detailing a dynamic frictional contact involving thermo-viscoelastic materials characterized by long memory and damage. The contact is modeled by the normal compliance condition with Coulomb's friction law, while surface wear is also factored in. The model was in the form of a coupled system which includes an evolution equation written in inclusion form for the frictional contact, parabolic variational inequality for the damage field, nonlinear differential equation for the temperature field and an equation for the wear particles and an evolution. A variational formulation for the model was derived and the existence of the unique weak solution established, under smallness assumptions on a part of the problem data. The proof used various results from the theory of evolution inequalities and repeated fixed-point arguments.

• long-range dependence
• thermoviscoelasticity
• damages
• normal compliance
• Coulomb friction
• surface wear
• variational inequalities
• evolution inclusions
• existence of weak solutions
• uniqueness
• fixed point argument
• nonlinear heat equation

• Contact Mechanics and Variational Inequalities
• Thermoelastic and Magnetoelastic Phenomena
• Adhesion, Friction, and Surface Interactions
• long-range dependence
• thermoviscoelasticity
• damages
• normal compliance
• Coulomb friction
• surface wear
• variational inequalities
• evolution inclusions
• Computational Theory and Mathematics
• Mechanics of Materials
• Computer Science
• Engineering